Finite Math Examples

$(\frac{7}{12} x^{3} - \frac{1}{3} x - \frac{1}{6}) - (- \frac{1}{12} x^{3} + \frac{1}{5} x - \frac{1}{6})$

Simplify each term.

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Combine $\frac{7}{12}$ and $x^{3}$ .

$\frac{7 x^{3}}{12} - \frac{1}{3} x - \frac{1}{6} - (- \frac{1}{12} x^{3} + \frac{1}{5} x - \frac{1}{6})$

Combine $x$ and $\frac{1}{3}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{1}{12} x^{3} + \frac{1}{5} x - \frac{1}{6})$

Simplify each term.

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Combine $x^{3}$ and $\frac{1}{12}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3}}{12} + \frac{1}{5} x - \frac{1}{6})$

Combine $\frac{1}{5}$ and $x$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3}}{12} + \frac{x}{5} - \frac{1}{6})$

To write $- \frac{x^{3}}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3}}{12} \cdot \frac{5}{5} + \frac{x}{5} - \frac{1}{6})$

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3}}{12} \cdot \frac{5}{5} + \frac{x}{5} \cdot \frac{12}{12} - \frac{1}{6})$

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{x^{3}}{12}$ by $\frac{5}{5}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3} \cdot 5}{12 \cdot 5} + \frac{x}{5} \cdot \frac{12}{12} - \frac{1}{6})$

Multiply $12$ by $5$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3} \cdot 5}{60} + \frac{x}{5} \cdot \frac{12}{12} - \frac{1}{6})$

Multiply $\frac{x}{5}$ by $\frac{12}{12}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3} \cdot 5}{60} + \frac{x \cdot 12}{5 \cdot 12} - \frac{1}{6})$

Multiply $5$ by $12$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (- \frac{x^{3} \cdot 5}{60} + \frac{x \cdot 12}{60} - \frac{1}{6})$

Combine the numerators over the common denominator.

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{- x^{3} \cdot 5 + x \cdot 12}{60} - \frac{1}{6})$

Simplify the numerator.

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Factor $x$ out of $- x^{3} \cdot 5 + x \cdot 12$ .

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Factor $x$ out of $- x^{3} \cdot 5$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- x^{2} \cdot 5) + x \cdot 12}{60} - \frac{1}{6})$

Factor $x$ out of $x \cdot 12$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- x^{2} \cdot 5) + x (12)}{60} - \frac{1}{6})$

Factor $x$ out of $x (- x^{2} \cdot 5) + x (12)$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- x^{2} \cdot 5 + 12)}{60} - \frac{1}{6})$

Multiply $5$ by $- 1$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- 5 x^{2} + 12)}{60} - \frac{1}{6})$

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- 5 x^{2} + 12)}{60} - \frac{1}{6} \cdot \frac{10}{10})$

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- 5 x^{2} + 12)}{60} - \frac{10}{6 \cdot 10})$

Multiply $6$ by $10$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - (\frac{x (- 5 x^{2} + 12)}{60} - \frac{10}{60})$

Combine the numerators over the common denominator.

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{x (- 5 x^{2} + 12) - 10}{60}$

Simplify the numerator.

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Apply the distributive property.

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{x (- 5 x^{2}) + x \cdot 12 - 10}{60}$

Rewrite using the commutative property of multiplication.

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x \cdot x^{2} + x \cdot 12 - 10}{60}$

Move $12$ to the left of $x$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x \cdot x^{2} + 12 \cdot x - 10}{60}$

Multiply $x$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 (x^{2} x) + 12 \cdot x - 10}{60}$

Multiply $x^{2}$ by $x$ .

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Raise $x$ to the power of $1$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 (x^{2} x^{1}) + 12 \cdot x - 10}{60}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x^{2 + 1} + 12 \cdot x - 10}{60}$

Add $2$ and $1$ .

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x^{3} + 12 \cdot x - 10}{60}$

$\frac{7 x^{3}}{12} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Find the common denominator.

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Multiply $\frac{7 x^{3}}{12}$ by $\frac{5}{5}$ .

$\frac{7 x^{3}}{12} \cdot \frac{5}{5} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $\frac{7 x^{3}}{12}$ by $\frac{5}{5}$ .

$\frac{7 x^{3} \cdot 5}{12 \cdot 5} - \frac{x}{3} - \frac{1}{6} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $\frac{x}{3}$ by $\frac{20}{20}$ .

$\frac{7 x^{3} \cdot 5}{12 \cdot 5} - (\frac{x}{3} \cdot \frac{20}{20}) - \frac{1}{6} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $\frac{x}{3}$ by $\frac{20}{20}$ .

$\frac{7 x^{3} \cdot 5}{12 \cdot 5} - \frac{x \cdot 20}{3 \cdot 20} - \frac{1}{6} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{7 x^{3} \cdot 5}{12 \cdot 5} - \frac{x \cdot 20}{3 \cdot 20} - (\frac{1}{6} \cdot \frac{10}{10}) - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{7 x^{3} \cdot 5}{12 \cdot 5} - \frac{x \cdot 20}{3 \cdot 20} - \frac{10}{6 \cdot 10} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Reorder the factors of $12 \cdot 5$ .

$\frac{7 x^{3} \cdot 5}{5 \cdot 12} - \frac{x \cdot 20}{3 \cdot 20} - \frac{10}{6 \cdot 10} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $5$ by $12$ .

$\frac{7 x^{3} \cdot 5}{60} - \frac{x \cdot 20}{3 \cdot 20} - \frac{10}{6 \cdot 10} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $3$ by $20$ .

$\frac{7 x^{3} \cdot 5}{60} - \frac{x \cdot 20}{60} - \frac{10}{6 \cdot 10} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Multiply $6$ by $10$ .

$\frac{7 x^{3} \cdot 5}{60} - \frac{x \cdot 20}{60} - \frac{10}{60} - \frac{- 5 x^{3} + 12 x - 10}{60}$

Combine the numerators over the common denominator.

$\frac{7 x^{3} \cdot 5 - x \cdot 20 - 10 - (- 5 x^{3} + 12 x - 10)}{60}$

Simplify each term.

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Multiply $5$ by $7$ .

$\frac{35 x^{3} - x \cdot 20 - 10 - (- 5 x^{3} + 12 x - 10)}{60}$

Multiply $20$ by $- 1$ .

$\frac{35 x^{3} - 20 x - 10 - (- 5 x^{3} + 12 x - 10)}{60}$

Apply the distributive property.

$\frac{35 x^{3} - 20 x - 10 - (- 5 x^{3}) - (12 x) - - 10}{60}$

Simplify.

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Multiply $- 5$ by $- 1$ .

$\frac{35 x^{3} - 20 x - 10 + 5 x^{3} - (12 x) - - 10}{60}$

Multiply $12$ by $- 1$ .

$\frac{35 x^{3} - 20 x - 10 + 5 x^{3} - 12 x - - 10}{60}$

Multiply $- 1$ by $- 10$ .

$\frac{35 x^{3} - 20 x - 10 + 5 x^{3} - 12 x + 10}{60}$

Simplify terms.

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Combine the opposite terms in $35 x^{3} - 20 x - 10 + 5 x^{3} - 12 x + 10$ .

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Add $- 10$ and $10$ .

$\frac{35 x^{3} - 20 x + 5 x^{3} - 12 x + 0}{60}$

Add $35 x^{3} - 20 x + 5 x^{3} - 12 x$ and $0$ .

$\frac{35 x^{3} - 20 x + 5 x^{3} - 12 x}{60}$

Add $35 x^{3}$ and $5 x^{3}$ .

$\frac{40 x^{3} - 20 x - 12 x}{60}$

Subtract $12 x$ from $- 20 x$ .

$\frac{40 x^{3} - 32 x}{60}$

Factor $8 x$ out of $40 x^{3} - 32 x$ .

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Factor $8 x$ out of $40 x^{3}$ .

$\frac{8 x (5 x^{2}) - 32 x}{60}$

Factor $8 x$ out of $- 32 x$ .

$\frac{8 x (5 x^{2}) + 8 x (- 4)}{60}$

Factor $8 x$ out of $8 x (5 x^{2}) + 8 x (- 4)$ .

$\frac{8 x (5 x^{2} - 4)}{60}$

Cancel the common factor of $8$ and $60$ .

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Factor $4$ out of $8 x (5 x^{2} - 4)$ .

$\frac{4 (2 x (5 x^{2} - 4))}{60}$

Cancel the common factors.

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Factor $4$ out of $60$ .

$\frac{4 (2 x (5 x^{2} - 4))}{4 (15)}$

Cancel the common factor.

$\frac{4 (2 x (5 x^{2} - 4))}{4 \cdot 15}$

Rewrite the expression.

$\frac{2 x (5 x^{2} - 4)}{15}$